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Question

A function f:RR is defined as f(x)=x3+3x22x+4. Which of the following is true about the function f(x)?

A
f(x) is an onto function
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B
f(x) is an into function
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C
f(x) is a one one function
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D
f(x)=4 will have only one solution
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Solution

The correct option is A f(x) is an onto function
As f(x) is a cubic polynomial,
Range of f(x) is R.
So, f(x) is an onto function.

f(x)=4x3+3x22x+4=4x(x23x+2)=0x(x1)(x2)=0
f(x)=4 has three solutions.
Hence, f(x) is a many-one function.

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